Carleman estimates and absence of embedded eigenvalues

TL;DR

This paper proves the absence of embedded eigenvalues for certain Schroedinger operators using novel Carleman estimates, extending results to variable coefficient operators with long-range and gradient potentials.

Contribution

Introduces new Lp Carleman estimates to demonstrate the nonexistence of embedded eigenvalues, extending previous dispersive estimate techniques to more general operators.

Findings

No embedded eigenvalues for Schroedinger operators with potentials in L^{(n+1)/2}

Extension of methods to variable coefficient operators with long-range and gradient potentials

Development of a new analytical framework using Carleman estimates

Abstract

Let L be a Schroedinger operator with potential W in L^{(n+1)/2}. We prove that there is no embedded eigenvalue. The main tool is an Lp Carleman type estimate, which builds on delicate dispersive estimates established in a previous paper. The arguments extend to variable coefficient operators with long range potentials and with gradient potentials.